How many litres of water should be added to a 30 litre mixture of milk and water containing milk and water in the ratio of 7 : 3 such that the resultant mixture has 40% water in it?

Question: How many litres of water should be added to a 30 litre mixture of milk and water containing milk and water in the ratio of 7 : 3 such that the resultant mixture has 40% water in it?

Solution:
And quantity of water in the mixture
= 3/(7 + 3) × 30 litres
= 9 litres.

Let water to be mixed 'a' litre
Then,
(30 + a) × 40/100 = 9 + a
⇒ 120 + 4a = 90 +10a
⇒ 120 - 90 = 10a - 4a
⇒ 30 = 6a
⇒ 6a = 30
∴ a = 5

Hence, 5 litres water mixed in the mixture.